Fraud and Felony are probably right, but there can be additional things as well. To a degree it depends if these are door-to-door solicitors or if they are working out of an office and doing mailings.
If they are going door-to-door they will likely need a vending license from the city or county, to simply come to the door and solicit. In my county, if they ring and they are not carrying the proper documentation, they can be arrested.
As for the percentage of $$ that goes to “overhead” versus the charity – it’s not necessarily fraud. It’s probably unethical, but if the charity fills out the appropriate 501-c-3 documentation, there is NOT a law that says they have to spend a certain percentage on the charity for which they are collecting.
However, there are various charity evaluation websites that do that sort of work, and anyone planning to donate ought to do their research.
Finally, in Atlanta, there are people that dress up in white nurse and doctor lab coats. They stand at street corners with cans what say “Give for sick children in Africa”. I imagine that that crowd (a) doesn’t have the permits to solicit and (b) isn’t registered as a charity with the state or the feds.
Bottom line – it may not necessarily be fraud, but there is usually reason to be suspicious.